document.write( "Question 488247: If we choose x from the set of values bigger than 0, is y = x² a function of x? explain
\n" );
document.write( "
\n" );
document.write( "If we choose y from the set of values bigger than 0, is y = x² a function of y? explain
\n" );
document.write( " \n" );
document.write( "
Algebra.Com's Answer #333328 by Theo(13342)![]() ![]() You can put this solution on YOUR website! y = x^2 makes y a function of x. \n" ); document.write( "the independent variable is x and the dependent variable is y. \n" ); document.write( "x^2 = y makes x^2 a function of y. \n" ); document.write( "the independent variable is y and the dependent variable is x^2. \n" ); document.write( "if we let z = x^2, then: \n" ); document.write( "x^2 = y becomes z = y \n" ); document.write( "z is considered a function of y because it depends on the value of y. \n" ); document.write( "you would solve this like you would solve any equation. \n" ); document.write( "if y = 5, then z = 5 \n" ); document.write( "since z = x^2, this means that x^2 = 5. \n" ); document.write( "suppose you had: \n" ); document.write( "x^2 = y-3 \n" ); document.write( "x^2 is still a function of y because it depends on the value of y. \n" ); document.write( "if y = 5, x^2 = y - 3 = 5 - 3 = 2 \n" ); document.write( "you get x^2 = 2 when y = 5 \n" ); document.write( "i believe this to be true, but i won't swear to it. \n" ); document.write( "there may be some rule that says you can't do this, but i haven't seen it. \n" ); document.write( "in practice, you can set anything equal to anything else. \n" ); document.write( "the dependent variable is a function of the independent variable. \n" ); document.write( "the equation determines the value of the dependent variable based on the value of the independent variable. \n" ); document.write( "x^2 is a function of y meets that definition. \n" ); document.write( "the value of x^2 is dependent on the value of y. \n" ); document.write( "the right side of that equation doesn't have to be just y. \n" ); document.write( "it can be any expression involving y. \n" ); document.write( "x^2 = y^3 + 5y - 3 would be an example. \n" ); document.write( "x^2 is a function of y. \n" ); document.write( "when y = 3, x^3 = 27 + 15 - 3 which becomes: \n" ); document.write( "x^2 = 39\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |